Finally, we apply the derived one-dimensional non-conservative scheme for two-dimensional advection equation using Strang splitting [1]}, [2]} that preserves the second order accuracy. Such treatment requires to solve only a given number of one-dimensional problems in alternating directions that can be solved by our proposed numerical scheme. One can show that such splitting scheme preserves the property of unconditional stability [2]} that is not the case of unsplitted version presented in [4]}.
